A circle passing through the intersection of the circles `x ^(2) + y^(2) + 5x + 4=0 and x ^(2) + y ^(2) + 5y -4 =0` also passes through the origin. The centre of the circle is

The locus of the centre of the circle passing through the intersection of the circles x^(2)+y^(2)=1 and x^(2)+y^(2)-2x+y=0 is

Find the equation of the circle passing through the intersection of the circles x^(2)+y^(2)-4=0 and x^(2)+y^(2)-2x-4y+4=0 and touching the line x+2y=0

Find the equation of circle passing through the origin and cutting the circles x^(2) + y^(2) -4x + 6y + 10 =0 and x^(2) + y^(2) + 12y + 6 =0 orthogonally.

Find the equation of the circle passing through the point of intersection of the circles x^(2)+y^(2)-6x+2y+4=0,x^(2)+y^(2)+2x-4y-6=0 and with its centre on the line y=x

A circle passes through the points of intersection of the line x=0 and the circle x^(2)+y^(2)+2x=3. If this circle passes through (sqrt(3),0) then its centre is :

Equation of the circle touching the circle x^(2) + y^(2) -15x + 5y =0 at ( 1,2) and also passing through the point (0,2) is :

Find the equation of the circle which cuts the circles x^(2)+y^(2)-9x+14=0 and x^(2)+y^(2)+15x+14=0 orthogonally and passes through the point (2,5)

(i) A circle whoe centre is the point of intersection of the line 2x - 3y + 4 - 0 and 3x + 4y - 5 = 0 passes through the origin. Find its equation. (ii) Find the equation of the circle passing through the point (1,-1) and centre at the intersection of the lines (x -y) = 4 and 2x + 3y = -7.